The redshift at which
P96b find their z 2.4 candidates is close to the
peak redshift
of star formation in disk galaxies of z 1-2
(M96). These
sub-galactic-sized objects
likely existed throughout the entire redshift range z 1-4, and could have grown into
the luminous giant galaxies (ellipticals and early-type spirals) that we
see today through the process of repeated hierarchical merging (cf.
NW94). An
epoch-dependent merger
rate proportional to (1 + z)2.5 would result in a time
integral of ~ 10-20 mergers of
compact objects from z ~ 3.5 to z = 0
(B94). This process
of repeated merging would
have to be largely complete by z ~ 1 if ellipticals and
early-type spirals were in fact
formed from such subgalactic clumps, as their HST morphological counts
show little evolution since z 1
(Fig. 3;
D95,
O96,
Mu94). The 18 z 2.4 candidates could thus
have merged to produce a few L* galaxies today, given that
objects separated by several
hundred kiloparsecs will have many crossing times in the interval
z 2.39 to z = 0.
The total V606 luminosity for the 18 z 2.4 candidates is
MV -24.7 mag
at z 2.39
(Fig. 5b), which agrees rather well
with the combined luminosities of a
few typical L* galaxies today of MV -24.3 mag (again including the
expected ~ -2 mag from their
K-corrections plus evolution,
W91).

In models of hierarchical galaxy formation, the luminous galaxies we see
today were
built up through the repeated merging of smaller protogalactic
pieces. Such subgalactic clumps appear to have been found at z 2.4 by
P96b and
P97. In
addition, there
have been recent reports of high redshift, "normal" star-forming
galaxies with possibly larger scale-lengths and higher luminosities (e.g.,
H96,
G94,
S96a,
F97,
Low97,
Tr97).
About 40-50% of the
S96a,
b &
Low97 samples are
Ly emitters, the
remainder are Ly
absorbers or show no Ly at all,
and may be more extinguished by dust and possibly
be a more evolved population of objects that has gone through more
generations of star-formation. The relatively stronger
Ly emitters like the
subgalactic clumps of
P96b and
the objects of H96,
Y96, and
F97
may have had fewer generations of O stars, and so fewer
supernovae to produce significant dust to resonantly scatter the
Ly light. These findings
suggest that galaxies likely formed over a large range of redshift
rather than at one special
time, and likely according to several different formation scenarios. If
a large percentage
of galaxies did in fact form hierarchically, one would expect to find
their building blocks
at high redshifts (z > 1-2), consistent with the large number of
star-forming objects
currently being found at such high redshifts. Many studies seem to point
toward a
merger rate that was significantly higher in the past, following
(1 + z)m
with m 2-3
(B94),
and suggesting that there must have been many more subgalactic
clumps around
at earlier epochs in order to produce the observed local luminosity
function. Taken
together with the fact that most luminous early-type galaxies appear to
have been "in place" by z ~ 1
(Mu94,
D95a,
O96,
L95,
H97), these two points
imply that a large
fraction of today's luminous ellipticals and early- to mid-type spirals
formed at z 1,
possibly from the merging of these sub-galactic sized objects. Indeed,
it has been shown
that disks can be regenerated (or generated) after such mergers
(HM95).

Currently, eight z 2.4
candidates have been spectroscopically confirmed with the
MMT or the KPNO 4 meter out of the 17 candidates surrounding 53W002
(P96b). In
total, there are two negative confirmations. Deeper Keck spectroscopy is
presented by
A97
on the F410M fields. If one assumes this same
70% success rate for the
Cycle 6
parallel fields, for which spectroscopy is in progress, then the yield
will be about two
z 2.4 candidates (out
of the three candidates found) from the 21-hour field and about
eight z 2.4 candidates
(out of the 12 candidates found) from the 16-hour field. The
latter is consistent with the 53W002 field, while the former has a much
lower density,
given the relative exposure times. The difference in the numbers of
candidates from the
two (approximately) equally-deep Cycle 6 F410M fields is only
significant at the ~ 2
level. There are two possible reasons for this discrepancy. First, it
may be an indication
that the 53W002 region is not representative for the general field, but
that it could be
a ~ 2 fluctuation compared to
other random fields, based on the numbers estimated
above (see P97).
Given that the Cycle 6 parallel F410M fields are only ~ 40% as deep as
the original 53W002 observations, one would expect to find 11-12
z 2.4 candidates in
any random part of the sky if these objects are indeed a widespread
population. If the
existence of the weak radio source or the other two z 2.4 AGN surrounding 53W002
(see Section 4) make the W02 field not
representative of the universe at z 2.4 then one should
find very few (if any) significant z 2.4 candidates in any of the
random F410M searches, not consistent with the number of z 2.4 candidates found in the
F410M parallel fields.
If there were large-scale structure at high-redshift as has been found
at z 1, one would
expect to find ~ 10 z 2.4 candidates in a random
field whose F410M line-of-sight is
approximately tangential to a sheet or passing through the intersection
of two sheets
or a particularly rich sheet, as possibly in 53W002 field. Conversely,
if one happens to
choose a field whose F410M line-of-sight passes in between sheets, one
should find very
few (although not necessarily zero) candidates, consistent with the
observed statistics. The F410M parallel fields of
P97
allow both of the latter possibilities.

As noted in P96b,
the confirmed 53W002 candidates show a remarkably
small velocity
dispersion (at z
2.391 ± 0.004 with v 286 km s-1,
corrected to z = 0), despite the much larger width of the F410M filter.
Ly emission could have been
seen in the F410M filter from objects at z 2.28-2.45, although some
dropoff in transmission would
occur for z 2.30
and z 2.42. This
implies that the subgalactic clumps may have
existed to some extent in groups or proto-clusters at high redshift, or
else we should have
seen a larger number of objects at other redshifts (z 2.391 ± 0.004) inside
the F410M
filter. Currently, only one object was found (out of eight) which has a
discrepant redshift
(z = 2.451), surprisingly far out into the red wing of the filter.

The 16-hour field could be a factor of 4-10x more dense than the 21-hour
field, far
in excess of any effect from its 1.2x greater F410M exposure time. The
variation in
number density among the Cycle 5 and 6 fields, if real, is indeed
suggestive of some kind
of structure (e.g., groups, clusters, or "sheets"). This structure may
have been hit with
the F410M filter "face-on" in the 53W002 and 16-hour fields, but we are
perhaps looking
"in between" any such major structures in the 21-hour field. A picture
is beginning to develop which is quite consistent with that of
RHS97, in which luminous
galaxies at z = 0 are broken up into several individual
Ly emitting chumps
at higher redshifts, and
are embedded in sheet-like structures, often lying along filaments or
ribbons where these sheets intersect (cf.
RHS97;
Ostriker, this volume). These sheets appear
to be group or
sub-cluster size, and may represent the preferred environment for
high-redshift objects.

The extremely narrow redshift distribution for the spectroscopically
confirmed objects
thus far (z 2.391
± 0.003), as compared to the much broader width of the F410M filter
(z = 0.12) leads one to
question why objects at other redshifts in the range 2.30
z 2.42 were not seen in
the MMT or KPNO spectroscopy samples thus far. There are
no major ground-based night-sky lines hampering the spectroscopic
follow-up around 4100 Å. There is good agreement of the space density
( 0.027 Mpc-3) and velocity
dispersion ( 286 km
s-1) of the objects with measured MMT & KPNO redshifts with
models based on the Press-Schechter theory (see Fig. 1 of
WF91) - which
predict the
abundance of dark-matter halos as a function of redshift - suggesting
that galaxies may
have existed preferentially in groups or "proto"-clusters at z 2.4. In redshift surveys
out to z 1
(B90;
Co94);
LF94),
and most recently to z 1
(CHS95a,
C96, Cohen et al.,
this volume) with the Keck 10-meter telescope, often more than a few
objects were found
at very similar redshifts in these small survey fields, supporting the
possible existence of
clumpiness in the redshift distribution in small fields out to z 1. In addition, groups
or other large structures have recently been found at redshifts
comparable to the
P96b
group (F96),
It is possible that the "spikes" or "frothiness" observed in the redshift
distribution of small fields out to z ~ 1 may have also existed
at some level out to
z ~ 1-3, although the clustering amplitude at higher redshift
would have to be lower
according to most CDM models. Recent deep KPNO 4m imaging in the F410M filter
(K97) and spectroscopy
(Co97)
shows that the that the 53W002 "cluster" stretches over
7'(~ 5 Mpc), with two more spectroscopic confirmations at z
2.39 (again out of an entire allowed redshift range of 233
z 2.46!), and may be part
of some larger-scale
structure at z
2.39. Further investigations are needed to see if such large scale
structure at these high redshifts are inconsistent with all CDM models.

It is possible that the
P96b
sub-galactic clumps, and possibly a large fraction of the
elusive primeval galaxies, may be hiding as many of the compact FBGs
(Fig. 1), and
have escaped proper recognition from the ground until now because they
are so small
and faint. The P96b
group of faint, compact star-forming subsystems at
z 2.39 could
thus be the galactic building blocks long sought after by proponents of
the 'bottom-up' galaxy formation models. Recent ground-based narrow-band
Ly imaging surveys
(TDT95)
may have missed any such groups or structures because the
filters used were
generally too narrow (~ 30 Å) to detect one by chance, unless some
previous knowledge
of the redshift already existed from, for example, one or more known
quasars or radio
galaxies. The WFPC2 medium-band filter F410M would sample
typically one or two such redshift structures (discussed in
Section 3.4.2) at z 2.39 (and is not limited by
sky-noise as most ground-based images are). Together with the extreme
compactness of the
P96bz 2.4 candidates,
this explains the higher detection rate of faint
Ly emitting
candidates with HST/WFPC2 in F410M.

Comparing the P96b
findings to those of CHS95a, one finds that about 5% of the faint
blue objects in the 53W002 WFPC2 field can be classified as 'chain
galaxies,' which is
lower than the 20%-50% estimated in their sample. We believe that such
objects are likely the short-lived
( 3 x 108
years out of a total of
5 x 109 years available for z 1) merger events among
time many faint blue sub-galactic clumps, in which the gas is
drawn out of the merging objects during the encounter
(NW94;
MH95).

Figure 7. Luminosity function of the Cycle 5 & 6
Ly emitting
candidates (filled triangles)
together with the LF at z ~ 2-3 in the HDF from
SLY97 (filled
squares). The data were
converted to AB magnitudes, and space densities were calculated using
the comoving volume
defined by the depth of the F410M passband and the size of the WFPC2
field at z 2.4. The
solid line is the best fit Schechter HDF LF of
SLY97. Dashed and dotted
lines are fiducial
photometric LFs of
SLY97
at z ~ 0.2-3. The Cycle 6 F410M
Ly LF
becomes incomplete for
MB
-18.5 mag.

3.4.4. The luminosity function of
Ly z
2.4 emitting candidates

The space density of the confirmed z 2.4 candidates from
P96b is ~
0.19 Mpc-3
(assuming a gravitationally-bound group). If one assumes a similar
velocity dispersion
for the Cycle 6 fields, the space densities would be ~ 0.064
Mpc-3 and ~ 0.29 Mpc-3 for
the 21-hour and 16-hour fields respectively. Making no assumptions about
the existence of any structure or groupings at z 2.4, the entire width of the
F410M filter is used
to derive a space density of subgalactic clumps for the 53W002 field
(again, assuming a
70% success rate) of ~
0.041 Mpc-3. In the same way, space densities are derived for
the Cycle 6 fields of ~ 0.0058 Mpc-3 and ~ 0.026
Mpc-3 for the 21-hour and 16-hour fields respectively.

The LF of the z 2.4
candidates was derived from the candidates in all three Cycles 5
and 6 fields together (Fig. 7), and binned
according to their F450W luminosities following
SLY97.
The z 2.4
Ly LF is quite steep
( ~ 1.8-2.0), despite the small-number
statistics involved.
SLY97
show a similar LF from photometric redshifts in the HDF that
changes with redshift, in agreement galaxy redshift surveys at z 1 (e.g.,
L95), showing
both a brightening and steepening with increasing redshift up to
z ~ 3, a result expected
in hierarchical models of galaxy formation in which merging plays an
important role in
removing the subgalactic clumps at lower redshifts. The LF at z 2.4 of
P97 is consistent
with that of the HDF for 2 < z < 3 (Fig. 8 of
SLY97), given the
following two caveats
from the F410M selection: (a) time completeness limit of
MF450WAB
-19.5 at z 2.4 is
imposed by the shallower F410M observations; and (b) given these
completeness limits in
F410M and B450, the F410M selection allows to only
detect significant Ly emitters,
not absorbers (the KPNO F410M images of
K97
are deeper compared to B, and do allow
to detect Ly absorbers).
According to the Keck spectroscopy of
S96a,
b and
Low97,
~ 40-50% of the higher luminosity U-band drop-out objects at
z = 2-3 have (weak)
Ly in emission. If we assume
the same fraction of
Ly emitters for the fainter z 2.4
candidates of P96a &
P97,
we may correct the F410M LF upwards by ~ 0.3
dex for the fact that it was selected by
Ly in emission only, which
would put the F410M points exactly on top of the
SLY97 LF at z 2-3.